State preparation and measurement in a quantum simulation of the O(3) sigma model

• URL: http://arxiv.org/abs/2006.15746v3
• Date: Tue, 22 Dec 2020 00:10:06 GMT
• Title: State preparation and measurement in a quantum simulation of the O(3) sigma model
• Authors: Alexander J. Buser, Tanmoy Bhattacharya, Lukasz Cincio, Rajan Gupta
• Abstract summary: We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
• Score: 65.01359242860215
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, Singh and Chandrasekharan showed that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. In a paper by the NuQS collaboration, the proposal is made to simulate such field theories on a quantum computer using the universal properties of a similar model. In this paper, following that direction, we demonstrate how to prepare the ground state of the model from and measure a dynamical quantity of interest, the O(3) Noether charge, on a quantum computer. In particular, we apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes and use shadow tomography to measure the dynamics of local observables. We then present and analyze a quantum algorithm based on non-unitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.

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